Order in the Chaotic region

  • Eduardo Piña
Part of the Lecture Notes in Physics book series (LNP, volume 189)


A simple algorithm is constructed for the quadratic one-parameter family of maps. It predicts the number of periodic orbits of arbitrary period ocurring for parameter values lower than any other corresponding to a given stable periodic orbit. This algorithm produces the number of periodic unstable points coexisting with the stable periodic orbit. This method associates an important polynomial in a one-to-one correspondence with the symbol of Metropolis et al. for ordering the periodic orbits, with the permutation matrix of the dynamics of points in the stable cycle, and with the matrix of regions separated by these points.

These polynomials coincide with those polynomials used by many authors in connection with the triangular map and with the topological entropy.


Periodic Orbit Characteristic Polynomial Periodic Point Topological Entropy Large Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Eduardo Piña
    • 1
    • 2
  1. 1.Departamento de FísicaUniversidad Autónoma MetropolitanaIztapalapa D. F.Mexico
  2. 2.Escuela Superior de Física y MatemáticasInstituto Politécnico NacionalZacatenco, D.F.México

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